Question: The sum of two numbers is $29$, and their difference is $3$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 29}$ ${x-y = 3}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 32 $ $ x = \dfrac{32}{2} $ ${x = 16}$ Now that you know ${x = 16}$ , plug it back into $ {x+y = 29}$ to find $y$ ${(16)}{ + y = 29}$ ${y = 13}$ You can also plug ${x = 16}$ into $ {x-y = 3}$ and get the same answer for $y$ ${(16)}{ - y = 3}$ ${y = 13}$ Therefore, the larger number is $16$, and the smaller number is $13$.